Free Printable GRADE 12 NAT Mathematics

1.

The diagram shows the first three patterns in a sequence in which each pattern has a square hole in the middle. If P(n) is the pattern that represents the number of small shaded squares given the nth figure, how many small shaded squares are needed to build the nth pattern of the sequence?

a)

P(n) = 6n + 14

b)

P(n) = 8n + 12

c)

P(n) = 10n + 10

d)

P(n) = 12n + 8

2.

On average, a person uses 2,200 paper napkins in one year. Which function calculates the number of paper napkins that the average person uses in x years, where N(x) is the number of napkins and x is the number of years?

a)

N(x) = 2200x

b)

N(x) = 2200/x

c)

N(x) = 2200 + x

d)

N(x) = 2000(5 − x)

3.

The graphs of f(x) = $2x^3 - 1$ and y = x are shown. Curve C is the graph of the inverse of f(x). Which statement is NOT true about curve C?

a)

The domain of f(x) is the range of $f^{-1}(x)$ .

b)

The inverse of f(x) is given by $f^{-1}(x) = \sqrt[3]{\frac{x+1}{2}}$ .

c)

The inverse of f(x) is given by $f^{-1}(x) = \frac{\sqrt[3]{x}}{2} + 1$ .

d)

f(x) and $f^{-1}(x)$ are symmetrical with respect to the line y = x.

4.

What can be said about the domain of $\frac{f(x)}{g(x)}$ if f(x) = 1 + $\sqrt{\phantom{x}}$ and g(x) = x − 3?

a)

It is given by the notation [2, +∞).

b)

It is given by the notation [2, 3) ∪ (3, +∞).

c)

It is the intersection of the domains of f(x) and g(x).

d)

It is the union of the domains of f(x) and g(x).

5.

Express the function $f(x)=\dfrac{x}{x^2-4}$ as a sum of 2 or more functions using the given functions r(x), s(x), and t(x) below: r(x) = $\dfrac{1}{x+2}$ , s(x) = $\dfrac{-2}{4 - x^2}$ , t(x) = $\dfrac{2x}{x^2-4}$ .

a)

f(x) = r(x) + t(x)

b)

f(x) = t(x) + s(x)

c)

f(x) = r(x) + s(x)

d)

f(x) = r(x) + s(x) + t(x)

6.

If $f(x)=x^2+2x+2$ , find a function g(x) for which $(f\circ g)(x)=x^2-4x+5$ .

a)

g(x) = x + 3

b)

g(x) = x − 3

c)

g(x) = x + 1

d)

g(x) = 1 − x

7.

Refer to the graph shown. Which method is applicable to determine the discontinuity of the function represented by the graph?

a)

Find the zeroes of the function.

b)

Locate the vertical asymptotes.

c)

Look at the horizontal asymptotes.

d)

Determine the range of the function.

8.

Consider the rational function $f(x)=\dfrac{3x^2-3x-6}{x^2+8x+16}$ . What is the vertical asymptote of the graph of f(x)?

a)

x = −4

b)

x = −1

c)

x = 2

d)

x = 4

9.

Consider the rational function $f(x)=\dfrac{3x^2-3x-6}{x^2+8x+16}$ . What are the intercepts of f(x)?

a)

x-intercepts are 1 and −2; y-intercept is $\dfrac{-3}{8}$ .

b)

x-intercepts are −1 and 2; y-intercept is $\dfrac{-3}{8}$ .

c)

x-intercepts are 1 and −2; y-intercept is $\dfrac{3}{8}$ .

d)

x-intercepts are −1 and 2; y-intercept is $\dfrac{3}{8}$ .

10.

Shaina has a smiley. She sends the smiley to 3 friends, with the instruction to pass on the smiley to three other friends, and so on. The figure illustrates the number of smileys until the third time that these are sent to friends as indicated by the 4th level. How many smileys will there be on the 5th time these smileys are sent to friends?

a)

81

b)

243

c)

729

d)

2187

11.

A lumber company has 1,800 trees. The owner aims to harvest 6% of the trees each year. Using the function formula $A(t)=a(1-r)^t$ , where a is the initial quantity and r is the rate over t years, which of the following equations represents the number of years it will take to harvest one-third of the trees?

a)

$\dfrac{1}{3}=(1-0.06)^t$

b)

$3=(1-0.06)^t$

c)

$600=1800(1-0.06)^t$

d)

$1800=600(1-0.06)^t$

12.

A lumber company has 1,800 trees and harvests 6% of the trees each year. How many years will it take to harvest one-third of the trees?

a)

About 9 years

b)

About 12 years

c)

About 15 years

d)

About 18 years

13.

The table shows a function f(x): x: 0, 1, 2, 3, 4, 5; f(x): 2, 6, 18, 54, 162, ?. What is f(5)?

a)

426

b)

446

c)

466

d)

486

14.

The volume of a cylinder is given by $V=\pi r^2 h$ , where r is the radius and h is the height. Suppose the height of the cylindrical can is 7 inches and the volume must be between $28\pi$ and $63\pi$ , inclusive. Which of the quadratic inequalities refers to the problem?

a)

$r^2\ge4\ \text{or}\ r^2\le9$

b)

$4\le r^2\le9$

c)

$r^2>4\ \text{or}\ r^2<9$

d)

$4<r^2<9$

15.

The volume of a cylinder is given by $V=\pi r^2 h$ , where r is the radius and h is the height. Suppose the height of the cylindrical can is 7 inches and the volume must be between $28\pi$ and $63\pi$ , inclusive. What are the possible values for the radius r (in inches)?

a)

$2\le r\le3$

b)

$2<r<3$

c)

$r\ge2\ \text{or}\ r\le3$

d)

$r>2\ \text{or}\ r<3$

16.

When all possible samples of a specific size are selected from the population, which statements about the distribution of sample means are correct? I. The mean of the sample means is equal to the population mean. II. The mean of the sample means is greater than the population mean. III. The standard deviation of the sample means is less than the standard deviation of the population.

a)

I

b)

II

c)

III

d)

I and II

e)

I and III

17.

Which of the following statements is NOT true about the sampling distribution of the sample proportions?

a)

The expected value for the sample proportion is the population proportion.

b)

The original parent distribution or the distribution of the sample data is the same as the sampling distribution.

c)

The shape of the distribution is approximately normal, provided the sample size is large enough where np and n(1 − p) are both at least 10.

d)

The standard error depends on the unknown population proportion that needs to be estimated.

18.

An international investor is considering opening a BPO in a certain district that does not have it. The investor will open that BPO only if there is evidence that more than 3,000 of the 12,000 residents in that district are qualified for the jobs. He commissioned a survey of 200 randomly selected residents and finds that 95 are qualified for the jobs. How will you state the null and alternative hypothesis to test the interest of the investor?

a)

$H_0: p\le0.25$ versus $H_a: p>0.25$

b)

$H_0: p\le0.475$ versus $H_a: p>0.475$

c)

$H_0: p\le30000$ versus $H_a: p>3000$

d)

$H_0: \mu\le30000$ versus $H_a: \mu>3000$

19.

Consider the propositions p: Alex is hardworking. q: Joan loves to travel. How do you express in symbols the proposition "It is not true that Joan loves to travel and Alex is not hardworking."?

a)

$\neg(q \land \neg p)$

b)

$q\lor p$

c)

$q\land p$

d)

$\neg q \lor p$

20.

Which of the following is NOT a valid argument? A. If Ralph eats a good breakfast, then he is attentive in class. Ralph was attentive in class. Therefore, Ralph ate a good breakfast. B. If Ralph eats a good breakfast, then he is attentive in class. Ralph ate a good breakfast. Therefore, he was attentive in class. C. Ralph eats a good breakfast, or he is attentive in class. Ralph did not eat a good breakfast. Therefore, he was attentive in class. D. If Ralph eats a good breakfast, then he is attentive in class. Ralph was not attentive in class. Therefore, Ralph did not eat a good breakfast.

a)

A

b)

B

c)

C

d)

D

21.

Let A and B be the propositions: A: Gadgets are helpful. B: Kelsey passed the subject. Which statement corresponds to $A\Rightarrow B$ ?

a)

Gadgets are not helpful or Kelsey passed.

b)

Gadgets are not helpful and Kelsey passed.

c)

Gadgets are not helpful or Kelsey did not pass.

d)

Gadgets are not helpful and Kelsey did not pass.

22.

Which of the following hypotheses is hoped to be rejected?

a)

Null hypothesis

b)

Alternative hypothesis

c)

Both A and B

d)

Neither A nor B

23.

A consumer wants to know if Brand A is more effective in washing dishes than Brand B. What is the null hypothesis $H_0$ for this test?

a)

Brand A is as effective as Brand B.

b)

Brand A is less effective than Brand B.

c)

Brand A is closely effective as Brand B.

d)

Brand A is more effective than Brand B.

24.

A consumer wants to know if Brand A is more effective in washing dishes than Brand B. What is the alternative hypothesis $H_a$ for this test?

a)

Brand A is as effective as Brand B.

b)

Brand A is as effective as Brand B.

c)

Brand A is less effective than Brand B.

d)

Brand A is more effective than Brand B.

25.

The following table contains the probability distribution for random variable x = the number of siblings that a SHS student has: X: 0, 1, 2, 3, 4, 5; P(X): 0.2, 0.3, 0.2, 0.1, 0.1, 0.1. What is the probability that a randomly selected SHS student has at most one sibling?

a)

0.2

b)

0.3

c)

0.5

d)

0.8

26.

The computed mean of the sibling distribution is 1.9. Which statement explains the meaning of this value?

a)

The average siblings of SHS students is 1.9.

b)

The average siblings of SHS students is 2.

c)

The mean number of siblings of SHS students is at least 1.

d)

The mean number of siblings of SHS students is at most 2.

27.

The standard deviation of a distribution is 7.17. Which of the following is/are NOT true about the standard deviation of the distribution? I. A small standard deviation suggests that the distribution of the random variable is quite concentrated around the mean. II. A large standard deviation suggests that the distribution is rather spread out, with some chance of observing values far from the mean.

a)

I only

b)

II only

c)

Both I and II

d)

Neither I nor II

28.

An estimator that is both accurate and precise is considered as “good”. Which of the following is a “good” estimator?

a)

Sample mode

b)

Sample mean

c)

Sample median

d)

Sample variance

29.

Situation: The mean score of thirty-five 12th graders in Science Quiz is 82 with a standard deviation $\sigma$ of $2.5$ . Which is the 95% confidence interval of the mean score of the 12th graders?

a)

$70<\mu<86$

b)

$79<\mu<85$

c)

$77<\mu<87$

d)

$81<\mu<89$

30.

Situation: The mean score of thirty-five 12th graders in Science Quiz is 82 with a standard deviation $\sigma$ of $2.5$ . Which is the best interpretation for a 95% confidence interval of the population mean?

a)

The average score of the 12th graders in Science Quiz is between 81 and 89 with 95%.

b)

The average score of the 12th graders in Science Quiz is between 70 and 86 with 95% confidence.

c)

The average score of the 12th graders in Science Quiz is between 77 and 87 with 95% confidence.

d)

The average score of the 12th graders in Science Quiz is between 79 and 85 with 95% confidence.

31.

Which of the following has the same meaning as $\log_{\tfrac{1}{5}} 320$ ?

a)

The product of $\tfrac{1}{5}$ and 320

b)

The power of 320 raised to $\tfrac{1}{5}$

c)

$\tfrac{1}{5}$ raised to a number yields 320

d)

A number raised to 320 that yields $\tfrac{1}{5}$

32.

Situation: The magnitude $R$ of an earthquake is given by $R=\tfrac{2}{3}\log\dfrac{E}{10^{4.40}}$ , where $E$ (in joules) is the energy released by the earthquake. What information should be provided in order to conclude that the magnitude of an earthquake is between 2 and 3?

a)

$\tfrac{2}{3}\log E$

b)

$\tfrac{2}{3}\log\log 10^{4.40}$

c)

magnitude $R$

d)

energy $E$ (in joules)

33.

Which of the following is correct?

a)

$\log_{2}x^{4}<4\log_{2}x$

b)

$\log_{2}x^{4}>1+4\log_{2}x$

c)

$\log_{2}2^{4}=(\log_{2})^{4}$

d)

$\log_{3}x^{2}=1+2\log_{3}x$

34.

Situation: The scores of four students in an eight-point quiz are 2, 3, 4, and 5. Assume that the four students constitute the population and all samples of size 2 are taken with replacement. What is the mean of the sample means?

a)

2.5

b)

3.5

c)

4.5

d)

5.5

35.

Situation: The scores of four students in an eight-point quiz are 2, 3, 4, and 5. Assume that the four students constitute the population and all samples of size 2 are taken with replacement. What is the variance of the sample means?

a)

0.255

b)

0.355

c)

0.438

d)

0.528

36.

Which statement is true about the mean of the sample means and the mean of the population?

a)

The mean of the sample means is equal to the mean of the population.

b)

The mean of the sample means is smaller than the mean of the population.

c)

The mean of the sample means is greater than the mean of the population.

d)

The mean of the sample means and the mean of the population are not related.

37.

How much interest is charged if an amount of Php 50,000 is loaned with an annual interest of 4.8% for 3 years?

a)

Php 7,200

b)

Php 22,000

c)

Php 57,000

d)

Php 72,000

38.

Jose loaned Php 500,000 in a bank to start a business. The loan amount would be paid in full after one year. If Jose paid Php 545,000 on time, what is the interest rate of the bank?

a)

1.09%

b)

8.26%

c)

9%

d)

10%

39.

Two banks offer to sell a two-story house to Mr. Fernando. Bank A offers a price of Php 3,200,000 that requires 20% down payment to be paid in 25 years. Bank B offers a price of Php 2,700,000 that requires 10% down payment to be paid in 15 years. Which plan offers a lesser annual mortgage?

a)

Bank A, because a bigger down payment will be deducted from the principal amount and the remaining amount will be divided by more years.

b)

Bank A, because a lesser down payment will be deducted from the principal amount, but the remaining amount will be divided by more years.

c)

Bank B, because a lesser down payment will be deducted from the principal amount, but the remaining amount will be divided by more years.

d)

Bank B, because a bigger down payment will be deducted from the principal amount and the remaining amount will be divided by more years.

40.

The value of a lot increases by 10.5% from its original price every year. If x denotes its original price, what mathematical expression refers to the lot’s value in y years?

a)

$x(0.105)^{y}$

b)

$x(1.105)^{y}$

c)

$xy(1.105)$

d)

$x(0.105)$

41.

The value of a car depreciates by 15% from its original price every year. Suppose that the car you bought is worth Php 850,000. What is the rounded price of the car after 4 years?

a)

Php 2,890,000

b)

Php 3,910,000

c)

Php 430,000.31

d)

Php 443,705.31

42.

Suppose that the population $y$ of a city doubles every 30 years. If the population started with 569, which of the following best models the situation?

a)

$569\,\big(2\big)^{\tfrac{x}{30}}$ , where $x=0$ corresponds to the time when the population is 569

b)

$569\,\big(2^{x}\big)^{30}$ , where $x=0$ corresponds to the time when the population is 569

c)

$569(30)\,2^{x}$ , where $x=0$ corresponds to the time when the population is 569

d)

$569\cdot 2\cdot 30\cdot x$ , where $x=0$ corresponds to the time when the population is 569

43.

Situation: Suppose that an amount of Php 25,000 is deposited in an account with a 2% interest rate compounded quarterly. Which of the following models the value of the deposited amount in any year?

a)

$25000(1+0.2)^{x}$

b)

$25000\Big(1+\dfrac{0.02}{4}\Big)^{x}$

c)

$25000\Big(1+\dfrac{0.2}{4}\Big)^{(4)(x)}$

d)

$25000\Big(1+\dfrac{0.02}{4}\Big)^{(4)(x)}$

44.

Situation: Suppose that an amount of Php 25,000 is deposited in an account with a 2% interest rate compounded quarterly. What will be the amount of money after 3 years?

a)

Php 25,376.88

b)

Php 26,541.94

c)

Php 43,200.00

d)

Php 44,896.41

45.

Joy buys a TV set that is payable in 6 months with 12% interest compounded quarterly. What would be the total amount paid if the principal amount of the TV set is Php 24,000.00?

a)

Php 24,940.00

b)

Php 25,461.60

c)

Php 25,520.00

d)

Php 25,926.40

46.

Which of the following are the intercepts of $y=\dfrac{5-x}{x-8}$ ?

a)

$(0,-\tfrac{5}{8})$ and $(5,0)$

b)

$(0,0)$ and $(5,-\tfrac{5}{8})$

c)

$(-\tfrac{5}{8},0)$ and $(0,5)$

d)

$(0,0)$ and $(-5,\tfrac{5}{8})$

47.

How many vertical asymptotes does the function $f(x)=\dfrac{x}{x^{2}-10x+25}$ have?

a)

0

b)

1

c)

2

d)

3

48.

Which of the following is the y-intercept of the graph of the rational function $f(x)=\dfrac{9-x^{2}}{x-3}$ ?

a)

$(-3,0)$

b)

$(0,-3)$

c)

$(0,3)$

d)

$(3,0)$

49.

Which of the following statements are the correct properties of a good estimator? I. The mean sample means equal to the mean of the population. II. As the sample size increases, the value of the estimator approaches the value of the parameter estimated. III. To estimate the parameter using Statistics, the relatively efficient estimator has the greatest variance.

a)

I and II

b)

I and III

c)

II and III

d)

I, II, and III

50.

Use the t-table provided. What is the t-value for a 90% confidence interval when the sample size is 21?

a)

1.721

b)

1.725

c)

1.717

d)

2.353

51.

Use the t-table provided. When the sample size is 21, what is the t-value for a 99% confidence interval?

a)

2.819

b)

2.831

c)

2.845

d)

5.841

52.

Situation: There are three marbles in a bag numbered 3, 5, and 7. One marble is selected at random, its number is noted, and then returned in the bag. If this experiment will be done many times, let $X$ be a random variable representing the number on the marble. What is the probability distribution of the random variable $X$ ?

a)

X: 7, 5, 3; P(X): 1/7, 1/7, 1/7

b)

X: 7, 5, 3; P(X): 1/5, 1/5, 1/5

c)

X: 3, 5, 7; P(X): 1/3, 1/3, 1/3

d)

X: 3, 5, 7; P(X): 1/2, 1/2, 1/2

53.

Situation: There are three marbles in a bag numbered 3, 5, and 7. One marble is selected at random, its number is noted, and then returned in the bag. If this experiment will be done many times, let $X$ be a random variable representing the number on the marble. What is the mean of the random variable $X$ ?

a)

3

b)

5

c)

7

d)

9

54.

Situation: There are three marbles in a bag numbered 3, 5, and 7. One marble is selected at random, its number is noted, and then returned in the bag. If this experiment will be done many times, let $X$ be a random variable representing the number on the marble. What is the variance of the random variable $X$ ?

a)

$4/3$

b)

$5/3$

c)

$7/3$

d)

$8/3$

55.

Joh is about to make a Php 1,000,000.00 loan. Bank A offers a loan with a simple interest of 8%; Bank B offers a loan with a 7.9% interest compounded semi-annually; and Bank C offers a loan under 7.8% interest compounded monthly. Which of the following statements is true?

a)

Interest in Bank A < interest in Bank B < interest in Bank C

b)

Interest in Bank B < interest in Bank A < interest in Bank C

c)

Interest in Bank C < interest in Bank B < interest in Bank A

d)

Interest in Bank C < interest in Bank A < interest in Bank B

56.

Emi loans Php 210,000.00 from a bank at an interest rate of $i$ , compounded semi-annually. After one year, the amount Emi needed to pay is Php 235,000.00. Which of the following is true?

a)

$i<10\%$

b)

$12\%<i$

c)

$10\%<i<11\%$

d)

$11\%<i<12\%$

57.

In computing the final amount of a loan with compound interest, we use the formula $F=P\big(1+\tfrac{r}{k}\big)^{kt}$ , where $P$ is the principal amount, $r$ is the annual rate, $k$ is the number of times the interest is compounded in a year, and $t$ is the number of years. Based on this formula, what would be true about the final amount of a loan worth Php 140,000.00 with an interest of 9% compounded three times a year, in 4 years?

a)

The final amount would be less than Php 150,000.00

b)

The final amount would be greater than Php 220,000.00

c)

The final amount would be greater than Php 200,000.00 but less than Php 220,000.00

d)

The final amount would be greater than Php 150,000.00, but less than Php 200,000.00

58.

A ball is dropped from a height of 10 meters. It bounces to $\frac{3}{5}$ of every preceding bounce height. What is the ball’s height in the fourth bounce?

a)

3.6 meters

b)

2.16 meters

c)

1.296 meters

d)

0.7776 meters

59.

Which of the following functions describes the table of values shown below? X: 1, 2, 3, 4 f(x): 32, 34, 38, 46

a)

$f(x)=30+2x$

b)

$f(x)=30+2^x$

c)

$f(x)=31+3^{x-1}$

d)

$f(x)=2x^2-4x+30$

60.

Which of the following is/are correct? I. $\log_2 64 = 6$ because $2^6=64$ II. $\log_{10} 100 = 10$ because $10\times10=100$ III. $\log_3 27 = 3$ because $3^3=27$ IV. $\log_{100} 100 = 0$ because $100^0=100$

a)

I only

b)

I and II

c)

I and III

d)

All except IV

GRADE 12 NAT Mathematics

Total questions: 60

Worksheet time: 30mins

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